Question

There are infinite rational numbers between two integers.
Please give reason in support of your answer

Answer 1

Answer:

yesss

Step-by-step explanation:

because for eg -1 and 2

between these no there are infinite rational no which are in the form of p/q

Answer 2

Answer:

Yes

Step-by-step explanation:

There are infinitely many rational numbers between  0  and  1 . At the very least, we have  1/n , where  n∈{2,3,4,…} . More can be constructed explicitly, but this will do.

Consider any two distinct rational numbers  a/b  and  c/d , where  ad≠bc .

We can bijectively map  a/b  to  0  and  c/d  to  1  by  f(x)=x−a/bc/d−a/b .

The inverse of  f  is  f−1(y)=a/b+(c/d−a/b)y , which maps  0  to  a/b  and  1  to  c/d .

Thus every distinct rational between  0  and  1  we can map to a distinct rational between  a/b  and  c/d . Since there are infinitely many in the first interval, there are infinitely many in the second.

There are other ways to construct further rational numbers between pairs of distinct rational numbers, such as taking the mean of the two, then taking the mean of the new number and one of the end points, and so on.